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6. Settlement of Shallow Footings CIV4249: Foundation Engineering Monash University CIV4249: Foundation Engineering Monash University

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Oedometer Test (change of) Height Applied Load Void Ratio Applied Stress Particular Sample Measurements: General Derived Relationship: h

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height vs time plots hohohoho height log time typically take measurements at 15s, 30s, 1m, 2m, 3m, 5m, 10m, 15m, 30m, 1h, 2h, 3h, 6h, 12h, 24h, 36h, 48h, 60h ….etc. elastic primaryconsolidation secondarycompression typically repeat for 12.5, 25, 50, 100, 200, 400, 800 and 1600 KPa

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Void ratio = f (h) RelativeVolumeSpecificGravity 1 e e e = 0.8 h = 1.9 cm dia = 6.0 cm W = g

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Elastic Settlement Instantaneous component Occurs prior to expulsion of water Undrained parameters Instantaneous component Expulsion of water cannot be separated Drained parameters Not truly elastic Clay Sand By definition - fully reversible, no energy loss, instantaneous Water flow is not fully reversible, results in energy loss, and time depends on permeability

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Elastic parameters - clay E u Soft clay Firm clay Stiff Clay V stiff / hard clay E u /c u most clays u All clays kPa kPa kPa kPa (no vol. change)

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Elastic parameters - sand E d Loose sandLoose sand Medium sandMedium sand Dense sandDense sand V dense sandV dense sand d Loose sandLoose sand Dense sandDense sand kPa kPa kPa kPa kPa kPa kPa kPa 0.1 to to to to 0.4 note volume change!

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Elastic Settlement = H /E = H. z E H zzzz Q Generalized stress and strain field E = z .dz 0

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Distribution of Stress r R z Q zzzz rrrr Boussinesq solution e.g. z = Q I z 2 z 2 I = [1+(r/z) 2 ] 5/2 2 [1+(r/z) 2 ] 5/2 I is stress influence factor

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Uniformly loaded circular area dddd dr r z load, q zzzz a By integration of Boussinesq solution over complete area: z = q [1- 1 ] = q.I [1+(a/z) 2 ] 3/2 [1+(a/z) 2 ] 3/2

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Stresses under rectangular area corner a uniformly loaded flexible rectangular area:Solution after Newmark for stresses under the corner of a uniformly loaded flexible rectangular area: Define m = B/z and n = L/zDefine m = B/z and n = L/z Solution by charts or numericallySolution by charts or numerically z = q.I I = 1 2mn(m 2 +n 2 +1) 1/2. m 2 +n 2 +2 m 2 +n 2 -m 2 n 2 +1 m 2 +n 2 -m 2 n 4 4 4 m 2 +n 2 +1 m 2 +n tan -1 2mn(m 2 +n 2 +1) 1/2 m 2 +n 2 -m 2 n 2 +1 m 2 +n 2 -m 2 n 2 +1 z zzzz B L

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Total stress change IIII z/B

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Computation of settlement 1. Determine vertical strains: r R z Q zzzz rrrr 2. Integrate strains: z = 1 [ z - ( r + )] E z = Q.(1+ ).cos 3 (3cos 2 -2 ) 2pz 2 E = z .dz 0 = Q (1- 2 ) rE rE

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Settlement of a circular area dddd dr r z load, q zzzz a Centre : Edge : = 4q(1- 2 ).a EEEE = 2q(1- 2 ).aE

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Settlement at the corner of a flexible rectangular area z zzzz B L Schleicher’s solution = q.B E IIII I = m ln + ln 1 1+ m m m+ m m = L/B

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Settlement at the centre of a flexible rectangular area B L B/2L/2 centre = 4q.B E IIII Superposition for any other point under the footing

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Settlement under a finite layer - Steinbrenner method q H B E “ Rigid ” X Y corner = q.B E IIII I = F 1 + F

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Superposition using Steinbrenner method B L

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Multi-layer systems q H1H1H1H1 B E1E1E1E1 “ Rigid ” H2H2H2H2 E2E2E2E2 = (H 1,E 1 ) + (H 1 +H 2,E 2 ) - (H 1,E 2 )

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A phenomenon which occurs in both sands and claysA phenomenon which occurs in both sands and clays Can only be isolated as a separate phenomenon in clays Expulsion of water from soils accompanied by increase in effective stress and strengthExpulsion of water from soils accompanied by increase in effective stress and strength Amount can be reasonably estimated in lab, but rate is often poorly estimated in lab Only partially recoverableOnly partially recoverable Primary Consolidation

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Total stress change IIII z/B

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Pore pressure and effective stress changes i f = u + At t = 0 : = u At t = : =

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Stress non-linearity q net z

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Soil non-linearity CrCrCrCr CcCcCcCc pcpcpcpc i f e vvvv = log + log C r H 1+e o C c H 1+e c p c i f p c

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Coeff volume compressibility (1+e o ).m v e vvvv = m v. . H

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Rate of Consolidation Flow h = H Flow h = H / 2 T = c v t i / H 2 U = 90% : T = 0.848

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Coefficient of Consolidation Coefficient of consolidation, c v (m 2 /yr)Coefficient of consolidation, c v (m 2 /yr) Notoriously underestimated from laboratory testsNotoriously underestimated from laboratory tests Determine time required for (90% of) primary consolidationDetermine time required for (90% of) primary consolidation Why?Why?

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Secondary Compression Creep phenomenonCreep phenomenon No pore pressure changeNo pore pressure change Commences at completion of primary consolidationCommences at completion of primary consolidation c /C c 0.05c /C c 0.05 c =c =c =c = eeee log (t 2 / t 1 ) = log (t 2 /t 1 ) cHcHcHcH (1+e p )

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Flexible vs Rigid stress stres s deflectiondeflection FF centre 0.8 centre RF = 0.8

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Depth Correction B z

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Total Settlement tot = RF x DF ( elas + pr.con + sec )

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Field Settlement for Clays (Bjerrum, 1962)

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Differential Settlements Guiding values Isolated foundations on clay< 65 mm Isolated foundations on sand<40 mm Structural damage to buildings1/150 (Considerable cracking in brick and panel walls) For the above max settlement values flexible structure<1/300 rigid structure<1/500

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Settlement in Sand via CPT Results (Schmertmann, 1970)

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